A deep learning-based approach to robust nonlinear model predictive control

Dealing with uncertainties is one of the most challenging issues that prevent nonlinear model predictive control (NMPC) from being a widespread reality. Many different robust schemes have been presented recently, such as multi-stage NMPC, in which the uncertainty is represented as a scenario tree. While multi-stage NMPC achieves promising performance in practice, it suffers from an exponential increase in complexity with the number of uncertainties considered making its real-time application difficult for large case studies. We suggest in this work to use multi-stage NMPC as a generator of data pairs that are used to learn the robust NMPC policy by means of deep neural networks. This choice is motivated by recent practical successes of deep learning and theoretical results that explain the improved representation capabilities of deep networks with respect to shallow networks. We present empirical evidence which shows that the use of deep neural networks with many hidden layers as opposed to shallow networks with only one significantly improves the learning process of a robust NMPC control law. These findings are illustrated with simulation studies of an industrial polymerization reactor.